Log Cabin Building

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©Copyright 1999 D F Curran

Order

Location

Cut time

Nails

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On a sunny Indian Summer day in late October Fishy decided to do some more work on the new hexagonal cabin he's been building. Picking a log from a set of six, each of which was a number of inches over 12' long: 1", 1.5", 2", 2.5", 3.5", or 4", he put one of these in place on one of the six sides, N, NE, NW, S, SE, or SW. Each log took a different amount of time to notch properly to fit: 18 minutes, 20 minutes, 24 minutes, 25 minutes, 30 minutes, or 32 minutes. And for each log he needed a different combination of nails to spike the log in depending on the thickness of the log and whether he was putting a window in that wall or not: two 9" nails, two 10" nails, two 12" nails, four 8" nails, four 10" nails, or four 12" nails. To get more sunlight in his cabin Fishy decided to put windows in three sides of his cabin using 4 nails instead of two for those sides. Can you determine the order of the logs, the nails used in each, the cutting time, which way way the logs faced, and which sides will have windows?

1) The log Fishy put in first was exactly two inches longer than the log Fishy put in the NW side of the cabin. Fishy spiked the log in place that took him 32 minutes to notch with his chain saw by drilling holes and using nails less than 10 inches long. The fourth log that Fishy spiked into place took more time to cut than the second log, but less time than the fifth log.

2) The log that ended up on the NW side took more time to cut than the log on the N side, but less time than the log on the NE side (which took less time to notch than the log on the S side ). There was a half-inch difference in some order between the length of the log Fishy used the four 10" nails on and the length of the log Fishy used the four 8" nails on. Fishy used 32 inches of total nail length to spike the log that was 12' 2" long.

3) There was a two-minute difference exactly in the time it took Fishy to cut the SW facing log and the SE facing log in some order. The third log Fishy put into place took exactly 5 minutes longer to cut than the log Fishy used two 9" nails to spike. There was more than a 10-minute difference between the time it took to notch the log that was 12' 4" and the time it took to notch the log that was 12' 1" in some order.

4) The log that measured 12' 1.5" was put into place immediately after the log that took 32 minutes to cut. The log that measured 12' 2.5" was put in place after the log that measured 12' 4", but before the log that measured 12' 2". The log Fishy spent 25 minutes notching (which was followed immediately by the log that faced SE) was put in place immediately after the log that he used two 12" nails on.

5) The cut time of the log that measured 12' 3.5" was 6 minutes longer than the log that faced N. Measuring the length of each of the nails he used and adding them together Fishy found he used more nail inches in total on the SE facing log than he did on the SW facing log. The fifth log Fishy put into place was longer than the sixth log. The log that took 18 minutes to notch was longer than the log that took two 10" nails. Fishy put the SW log in place sometime after he put the SE log in place.

6) Of course Fishy had been working on this cabin before this day--he was simply adding to it. The last log he put in place was, of course, in the position of the highest log in the cabin at the time he started. The two adjacent to it and the one directly opposite to it were at the same level, which was one log lower than the log in the position of the last log he put on. The remaining two were at one level lower than the logs adjacent to it, and two levels lower than the one in the position of the last log Fishy put on. Fishy could only add logs onto two logs that were equal in height.

Solution

DAVE'S LOGIC PUZZLES